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Creating Functions

Creating Functions. Functional Programming. The function calculator. Functional programming is all about using functions Functions are first class Take as input, return as result, store in data A functional language is a function calculator What buttons do we have for “creating” functions?.

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Creating Functions

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  1. Creating Functions Functional Programming

  2. The function calculator • Functional programming is all about using functions • Functions are first class • Take as input, return as result, store in data • A functional language is a function calculator • What buttons do we have for “creating” functions?

  3. 12 ways to get a new function • By defining one at top level • By equation • By cases • By patterns • By local definition (where and let) • By use of a library • By lambda expression (anonymous functions) • By parenthesizing binary operators • By section • By currying (partial application) • By composition • By combinator (higher order functions) • By using data and lookup (arrays lists and finite functions)

  4. By defining at top level Module Test where plus5 x = x + 5 last x = head(reverse x) CreatingFunctions> plus5 7 12 CreatingFunctions> last [2,3,4] 4

  5. By cases Vertical Bar Equal sign absolute x | x < 0 = -x | x >= 0 = x swap (x,y) | x < y = (x,y) | x > y = (y,x) | x==y = (x,y) Name and argument condition Value for case CreatingFunctions> absolute 3 3 CreatingFunctions> absolute (-4) 4 CreatingFunctions> swap (23,5) (5,23)

  6. By patterns Pattern may contain constructors. Constructors are always capitalized. True and False are constructors • Example on Booleans myandTrue False = False myandTrue True= True myandFalse False= False myandFalse True = False • Order Matters • Variables in Patterns match anything myand2 True True = True myand2 x y = False • What happens if we reverse the order of the two equations above?

  7. By local definition(where and let) ordered = sortBy backwards [1,76,2,5,9,45] where backwards x y = compare y x CreatingFunctions> ordered [76,45,9,5,2,1]

  8. By use of a Library smallest = List.minimum [3,7,34,1] CreatingFunctions> smallest 1

  9. By lambda expression (anonymous functions) CreatingFunctions> descending [76,45,9,5,2,1] CreatingFunctions> bySnd [[(1,'a'),(3,'a')],[(2,'c')]] descending = sortBy (\ x y -> compare y x) [1,76,2,5,9,45] bySnd = groupBy (\ (x,y) (m,n) -> y==n) [(1,'a'),(3,'a'),(2,'c')]

  10. By parenthesizing binary operators six:: Integer -- 1 + 2 + 3 + 0 six = foldr(+) 0 [1,2,3] CreatingFunctions> six 6

  11. By section add5ToAll = map (+5) [2,3,6,1] CreatingFunctions> add5ToAll [7,8,11,6]

  12. By partial application Note, both map and any, each take 2 arguments hasFour = any (==4) doubleEach = map (\ x -> x+x) CreatingFunctions> hasFour [2,3] False CreatingFunctions> hasFour [2,3,4,5] True CreatingFunctions> doubleEach [2,3,4] [4,6,8]

  13. By composition hasTwo = hasFour.doubleEach empty = (==0) . length CreatingFunctions> hasTwo [1,3] False CreatingFunctions> hasTwo [1,3,2] True CreatingFunctions> empty [2,3] False CreatingFunctions> empty [] True

  14. By combinator (higher order functions) k x = \ y -> x all3s = map (k 3) [1,2,3] CreatingFunctions> :t k True k True :: a -> Bool CreatingFunctions> all3s [3,3,3]

  15. Using data and lookup(arrays, lists, and finite functions) whatDay x = ["Sun","Mon","Tue","Wed","Thu","Fri","Sat"] !!x first9Primes = array (1,9) (zip [1..9] [2,3,5,7,11,13,17,19,23]) nthPrime x = first9Primes !x CreatingFunctions> whatDay 3 "Wed" CreatingFunctions> nthPrime 5 11

  16. When to define a higher order function? • Abstraction is the key mysum [] = 0 mysum (x:xs) = (+)x (mysumxs) myprod [] = 1 myprod (x:xs) = (*)x (myprodxs) myand [] = True myand (x:xs) = (&&)x (myandxs) • Note the similarities in definition and in use ? mysum [1,2,3] 6 ? myprod [2,3,4] 24 ? myand [True, False] False

  17. When do you define a higher order function? • Abstraction is the key mysum [] = 0 mysum (x:xs) = (+)x (mysum xs) myprod [] = 1 myprod (x:xs) = (*)x (myprod xs) myand [] = True myand (x:xs) = (&&)x (myand xs) • Note the similarities in definition and in use ? mysum [1,2,3] 6 ? myprod [2,3,4] 24 ? myand [True, False] False

  18. Abstracting myfoldrope [] = e myfoldrope (x:xs) = op x (myfoldrop exs) ? :t myfoldr myfoldr :: (a -> b -> b) -> b -> [a] -> b ? myfoldr (+) 0 [1,2,3] 6 ?

  19. Functions returned as values • Consider: k x = (\ y -> x) ? (k 3) 5 3 • Another Example: plusn n = (\ x -> x + n) ? (plusn 4) 5 9 • Is plusn different from plus? why? • plus x y = x + y

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